Exact Solutions for Some Unsteady Flows of non-Newtonian Fluids of Rate Type

Abstract

The main theme of this thesis is to establish exact solutions for certain flows of non- Newtonian fluids of rate type including Maxwell fluids, generalized Maxwell fluids and Oldroyd-B fluids. The rotational flow of a generalized Maxwell fluid in a circu- lar cylinder, oscillating flows between two coaxial infinite cylinders for Maxwell and Oldroyd-B fluids, as well as the flow induced in Maxwell fluids by a constantly accel- erating plate between two side walls perpendicular to the plate have been discussed here. The mathematical formulation of these problems leads to partial differential equations which are solved by different mathematical techniques like Laplace trans- form, Fourier sine transform and Hankel transform. The associated tangential stresses are also determined. By means of graphical illustrations, the required time to reach the steady-state for oscillating flows of Maxwell and Oldroyd-B fluids are also ob- tained. The solutions that have been obtained satisfy both the governing equations and all imposed initial and boundary conditions, the differentiating term by term into infinite sums being clearly permissible. Finally, the corresponding solutions for Newtonian fluids are also obtained as limiting cases.